公司理财试卷及答案

4.11 You have the opportunity to make an investment that costs $900,000. If you make this investment now, you will receive $120,000 one year from today, $250,000 and $800,000 two and three years from today, respectively. The appropriate discount rate for this investment is 12 percent.

a. Should you make the investment?

b. What is the net present value (NPV) of this opportunity?

c. If the discount rate is 11 percent, should you invest? Compute the NPV to support your answer.

a. The cost of investment is $900,000.

PV of cash inflows = $120,000 / 1.12 + $250,000 / 1.122 + $800,000 / 1.123

= $875,865.52

Since the PV of cash inflows is less than the cost of investment,

you should not make the investment.

b. NPV = -$900,000 + $875,865.52

= -$24,134.48

c. NPV = -$900,000 + $120,000 / 1.11 + $250,000 / 1.112 + $800,000 /

1.113

= $-4,033.18

Since the NPV is still negative, you should not make the investment.

4.24 Harris, Inc., paid a $3 dividend yesterday. If the firm raises its dividend at 5 percent every year and the appropriate discount rate is 12 percent, what is the price of Harris stock?

P = $3 (1.05) / (0.12 - 0.05) = $45.00

4.25 In its most recent corporate report, Williams, Inc., apologized to its stockholders for not paying a dividend. The report states that management will pay a $1 dividend next year. That dividend will grow at 4 percent every year thereafter. If the discount rate is 10 percent, how much are you willing to pay for a share of Williams, Inc.?

P = $1 / (0.1 - 0.04) = $16.67

4.51 Southern California Publishing Company is trying to decide whether or not to revise its popular textbook, Financial Psychoanalysis Made Simple. They have estimated that the revision will cost $40,000. Cash flows from increased sales will be $10,000 the first year. These cash flows will increase by 7 percent per year. The book will go out of print five years from now. Assume the initial cost is paid now and all revenues are received at the end of each year. If the company requires a 10 percent return for such an investment, should it undertake the revision?

The effective annual interest rate is

[ 1 + (0.08 / 4) ] 4 – 1 = 0.0824

The present value of the ten-year annuity is

= $5,974.24

PV = 900 10

.0

0824

Four remaining discount periods

PV = $5,974.24 / (1.0824) 4 = $4,352.43

5.13 A common stock pays a current dividend of $2. The dividend is expected to grow at an 8-percent annual rate for the next three years; then it will grow at 4 percent in perpetuity. The appropriate discount rate is 12 percent. What is the price of this stock?

Price = $2 (1.08) / 1.12 + $2 (1.082) / 1.122 + $2 (1.083) / 1.123

+ {$2 (1.083)(1.04) / (0.12 - 0.04)} / 1.123

= $28.89

5.17 Consider the stock of Davidson Company that will pay an annual dividend of $2 in the coming year. The dividend is expected to grow at a constant rate of 5 percent permanently. The market requires a 12-percent return on the company.

a. What is the current price of a share of the stock?

b. What will the stock price be 10 years from today?

a. P = $2 / (0.12 - 0.05) = $28.57

b. P10 = D11 / (r - g)

= $2 (1.0510) / (0.12 - 0.05)

= $46.54

Alternatively, given the answer to part a, P10 = P0(1+g)10 = 28.54(1.05)10 = $46.54.

5.20 Allen, Inc., is expected to pay an equal amount of dividends at the end of the first two years. Thereafter, the dividend will grow at a constant rate of 4 percent indefinitely. The stock is currently traded at $30. What is the expected dividend per share for the next year if the required rate of return is 12 percent?

$30 = D / 1.12 + D / 1.122 + {D (1 + 0.04) / (0.12 - 0.04)} / 1.122 = 12.053571 D

D = $2.49

5.21 Calamity Mining Company's reserves of ore are being depleted, and its costs of recovering a declining quantity of ore are rising each year. As a result, the company's earnings are declining at the rate of 10 percent per year. If the dividend per share that is about to be paid is $5 and the required rate of return is 14 percent, what is the value of the firm's stock?

[Insert before last sentence of question: Assume that dividends are a fixed proportion of earnings.]

Dividend one year from now = $5 (1 - 0.10) = $4.50

Price = $5 + $4.50 / {0.14 - (-0.10)}

= $23.75

Since the current $5 dividend has not yet been paid, it is still included in the stock price.

5.25 Rite Bite Enterprises sells toothpicks. Gross revenues last year were $3 million, and total costs were $1.5 million. Rite Bite has 1 million shares of common stock outstanding. Gross revenues and costs are expected to grow at 5 percent per year. Rite Bite pays no income taxes, and all earnings are paid out as dividends.

a. If the appropriate discount rate is 15 percent and all cash flows are received at year's end, what is the price per share of Rite Bite stock?